For
with and
, let
be the unique
subset of
such that
(mod ), where
is the
number of partitions of with parts in . Let be
an odd prime number, and let be irreducible of order ; i.e.,
is the smallest positive integer such that divides
in
. N. Baccar proved that the elements of
of the form , where and is odd,
are given by the -adic expansion of a zero of some polynomial
with integer coefficients. Let be the order of
modulo , i.e., the smallest positive integer such that
(mod ). Improving on the method with which was obtained explicitly only when
, here we make explicit when
. For that, we have used the number of points of the elliptic curve
modulo .